Apparatus and process for determination of dynamic scan field curvature

ABSTRACT

A process for the determination of focal plane deviation uniquely due to the scanning dynamics associated with a photolithographic scanner is described. A series of lithographic exposures is performed on a resist coated silicon wafer using a photolithographic scanner. The lithographic exposures produce an array of focusing fiducials that are displaced relative to each other in a unique way. The resulting measurements are fed into a computer algorithm that calculates the dynamic scanning field curvature in an absolute sense in the presence of wafer height variation and other wafer/reticle stage irregularities. The dynamic scan field curvature can be used to improve lithographic modeling, overlay modeling, and advanced process control techniques related to scanner stage dynamics.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to processes for semiconductormanufacturing and, more particularly, to optical lithography techniquesfor the determination of focal plane deviation (FPD) associated withphotolithographic projection systems.

2. Description of the Related Art

Semiconductor manufacturers and lithography tool vendors have beenforced to produce higher numerical aperture (NA) lithography systems(steppers or scanners) using smaller wavelengths (for example, 193 nmDUV lithography) in response to the semiconductor industry's requirementto produce ever-smaller critical features. See, for example, thestatement of the well-known “Moore's Law” at “Cramming more componentsonto integrated circuits”, G. Moore, Electronics, Vol. 38, No. 8, 1965.The ability to produce (manufacture) sub-wavelength features can oftenbe determined by considering the rather simple (3-beam) Rayleigh scalingResolution (R) and (Reference A) Depth-of-Focus (DoF) equations; ˜λ/2NAand ˜λ/2NA² respectively. These coupled equations stress the inverserelationship between resolution and DoF based on the exposure wavelength(λ and numerical aperture (NA) for features printed near the limit ofthe optical system. High NA lithography has led to improved resolutionand a reduction in the overall focus budget, making lithographyprocesses difficult to control. See “Distinguishing dose from defocusfor in-line lithography control”, C. Ausschnitt, SPIE, Vol. 3677, pp.140-147, 1999; and “Twin Scan 100 Product Literature”, ASML). Poorlithographic process control (focus and exposure) leads to smallerproduct yields, increased manufacturing costs, and poor time to market.While semiconductor lithographers have discovered creative reticleenhancement techniques (RETs) and other optical techniques (PSM) toincrease the useable DoF—the problem remains. See, for example, “TheAttenuated Phase-Shifting Mask”, B. Lin, and “Method and Apparatus forEnhancing the Focus Latitude in Lithography”, Pei-Yang Yan, U.S. Pat.No. 5,303,002, Apr. 12, 1994. Therefore, it is crucial to monitor focusduring photolithographic processing and develop new methods for focuscontrol. Typically focus error across a scanner field can be attributedto the following three factors: 1) wafer and reticle non-flatness, 2)dynamic wafer/reticle stage error, and 3) static and/or dynamic lensfield curvature. For a photolithographic scanner, dynamic fieldcurvature varies in the cross scan direction (x) in rather complex ways.

The ability to precisely control the photolithographic scanner tooldepends on the ability to determine the magnitude and direction of theindividual focusing error components (items 1-3 above) and to accountfor repeatable and non-repeatable portions of those errors. Whilefocusing error causes reduction in image fidelity, the coupling of focuserror and other lens aberrations (distortions) degrades overlay orpositional alignment as well. See, for example, “Impact of LensAberrations on Optical Lithography”, T. Brunner.

Over the past 30 years the semiconductor industry has continued toproduce faster (via smaller critical features) and more complex (greaterfunctionality, dense patterning) circuits, year after year. See, forexample, “Optical Lithography—Thirty years and three orders ofmagnitude”, J. Bruning, SPIE, Vol. 3051, pp. 14-27, 1997; and “Crammingmore components onto integrated circuits”, supra. The push to smallerfeature sizes is gated by many physical limitations. See “Introductionto Microlithography”, L. Thompson et al., ACS 2nd Edition, p. 69, 1994.As the critical dimensions of semiconductor devices approach 50 nm, theusable DoF will approach 100 nm. See “2001 ITRS Roadmap”, SEMATECH, pp.1-21). Continued advances in lithography equipment (higher NA systems,smaller wavelength exposure sources), RET's, resist processing, andautomated process (focus and exposure) control techniques will get moredifficult and remain critical. See, for example, “2001 ITRS Roadmap”,supra; and “The Waferstepper Challenge: Innovation and Reliabilitydespite Complexity”, Gerrit Muller, Embedded Systems InstituteNetherlands, pp. 1-11, 2003. Finally, while FPD deviation can bedetermined using a variety of methods, none of these methods have theability to divide the focal error into correctable (possibly systematic)and non-correctable (possibly random) portions—especially for scannersand to further decouple the effects of wafer flatness. The ability todecouple focus error leads directly to improved dynamic scanningbehavior using a variety of advanced process control techniques. See“Predictive process control for sub-0.2 um lithography”, T. Zavecz, SPIEML, Vol. 3998-48, pp. 1-12, 2000; “TWINSCAN 1100 Product Literature”,supra; and “Advanced statistical process control: Controlling sub-0.18μm Lithography and other processes”, A. Zeidler et al., SPIE, Vol. 4344,pp. 312-322, 2001.

It should be noted that, even if a perfect lens with no dynamic lensfield curvature (ZL=0) could be obtained, the lens could still beassociated with FPD due to scanner dynamic focal plane deviation (SFPD),which is the scanner field curvature error associated with stagesynchronization error in the Z direction. Thus, in view of the industrytrends described above, more precise techniques for determining FPD andSFPD are continuously desired.

FPD: There are a number of methods that with greater or lesser accuracymeasure defocus or focal plane deviation (FPD) over an exposure field.In general terms, each of these techniques estimate the focal erroracross the field using a variety of special reticle patterns (focusingfiducials, FF), interferometric devices, mirrors, sensors, andstatistical models. In addition, each of these methods utilizes thestepper or scanner wafer stage leveling and positioning system and/oroptical alignment system to aid in the determination of FPD. See, forexample, “TWINSCAN 1100 Product Literature”, supra. The term “FPD” is arather general term describing the complete focus error associated withthe photolithographic stepper or scanner, deviations from the focalplane in reference to the wafer surface. Among other things, FPD can becaused by lens tilt, stage/reticle tilt, reticle bow, lens fieldcurvature, and stage synchronization error. FIG. 7 shows a genericphotolithographic leveling system. FIG. 8 illustrates some commonreticle patterns (e.g. IBM's Phase Shift Focus Monitor (PSFM), andASML's FOCAL alignment mark) that are used to determine FPD for bothsteppers and scanners. Typically, FPD calibration/monitoring isperformed daily or at least weekly to ensure that the stepper or scanneris operating within design limits (verifying the focus system works, thestage is level, etc.). While both techniques are widely accepted bothtechniques require complex calibrations to be performed at each fieldpoint. See “Detailed Study of a Phase-Shift Focus Monitor”, G. Pugh etal., SPIE Vol. 2440, pp. 690-700, 1995; and “FOCAL: Latent ImageMetrology for Production Wafer Steppers”, P. Dirksen et al., SPIE, Vol.2440, p. 701, 1995).

Table 1 below lists some FPD prior art methods: TABLE 1 MeasurementMethod Type Comment ISI (See “Apparatus, Absolute Extremely Method ofMeasurement and accurate. Method of Data Analysis for Correction ofOptical System”, A. Smith et al., U.S. Pat. No. 5,828,455 issued Oct.27, 1998 and “Apparatus, Method of Measurement and Method of DataAnalysis for Correction of Optical System”, A. Smith et al., U.S. Pat.No. 5,978,085 issued Nov. 2, 1999) FOCAL (See “FOCAL: Latent RelativePublished Image Metrology for Production version claims Wafer Steppers”,supra) high absolute accuracy, resolution averaging in practice. IBMfocus monitor (See Absolute Requires “Optical Focus Phase Shift‘calibration’. Test Pattern, Monitoring System It is very and Process”,T. Brunner et process al., U.S. Pat. No. independent. 5,300,786 issuedApr. 5, 1994) Schnitzl (See “Distinguishing Relative Complex Dose fromDefocus for In-Line with one calibration, Lithography Control”, supra)exposure varying target sensitivity. TIS (See “193 Step and ScanRelative Relies on wafer Lithography”, G. Davies et Z-stage, al., SemiTech Symposium, Japan, accuracy/repeat. 1998; and “Twin Scan 1100Product Literature”, supra)

ISI (Litel): A method for determining the aberrations of an opticalsystem is described in U.S. Pat. No. 5,828,455, supra, and U.S. Pat. No.5,978,085, supra. Where a special reticle is used to determine theZernike coefficients for photolithographic steppers and scanners.Knowing the wavefront aberration (Zernike coefficients and theassociated polynomial) associated with the exit pupil of the projectionsystem includes information about the lens field curvature or focus(Zernike coefficient a4, for example). Smith uses a special reticle anda self-referencing technique to rapidly identify FPD to a high degree ofaccuracy, determines focusing errors to ˜5 nm, in the presence ofscanner noise. This method automatically determines lens field curvatureinformation for both static and dynamic exposure tools (steppers andscanners).

PSFM: A method (Phase Shift Focus Monitor) described in U.S. Pat. No.5,300,786, supra, can be used to determine and monitor the focal planedeviation (FPD) associated with the lithographic process. Moreinformation can be found in “Detailed Study of a Phase-Shift FocusMonitor”, supra. In general, an alternating PSM with phase close to 90°possesses unusual optical properties that can be exploited to measurefocus errors. See, for example, “Quantitative Stepper Metrology Usingthe Focus Monitor Test Mask”, T. Brunner et al., SPIE, Vol. 2197, pp.541-549; and “Using the Focus Monitor Test Mask to CharacterizeLithographic Performance”, R. Mih et al., SPIE, Vol. 2440, pp. 657-666,1995. It is possible to design a “box-in-box” overlay target using aphase shift mask pattern (referred to here as a focusing fiducial; seeFIGS. 8-9), in which the measured overlay error is proportional to thefocus error (see FIG. 10). Focal plane non-flatness is then determinedby measuring the focusing fiducials across the lens field. Astigmatisminformation appears as differences between the delta-X overlay error andthe delta-Y overlay error measurement. This technology has also beenused for assessing variations in focus across the wafer due to lensheating, misfocusing near the edge of the wafer, and chuck/stagenon-flatness. One major drawback with the PSFM method is that a fairlyelaborate calibration procedure (focus offset vs. overlay shift for eachfield point) is required before it can be used, the PSFM technique israther sensitive to the source-sigma (Na-source/Na-objective) thatvaries from process to process. Additional PSM techniques, such as thosefound in “Monitor for Alternating Phase Shift Masks”, L. Liebmann etal., U.S. Pat. No. 5,936,738 issued Aug. 10, 1999, are used in a similarway. While the PSFM method provides an FPD map across a scanner orstepper field it does not provide a method for determining the dynamiclens field curvature independent of wafer height variation in thepresence of stage synchronization error. See, for example,“Comprehensive Focus-Overlay-CD Correlation to IdentifyPhotolithographic Performance”, Dusa et al., SPIE, Vol. 2726-29, 1996.

FOCAL: A method (FOCAL—Focus determination using stepper alignmentsystem) described by P. Dirksen, et. al., SPIE, Vol. 2440, 1995, p. 701,specifies a focusing fiducial that can be used to find FPD andastigmatism across the exposure field (lens). FOCAL alignment marks(focusing fiducials) consist of modified wafer alignment marks that aremeasured using the stepper wafer alignment subsystem. See, for example,FIG. 1 of “FOCAL: Latent Image Metrology for Production Wafer Steppers”,P. Dirksen et al., SPIE, Vol. 2440, p. 701, 1995. Defocus of the toolresults in an apparent shift of the center of the alignment markrelative to that of the ‘best focus’ position. The FOCAL technique makesuse of the exposure tool's alignment mechanism and therefore requiresthat the stepper or scanner be off-line for the length of themeasurement sequence. FOCAL marks are sensitive to exposure and sigmalike the PSFM method; however, since fiducial response is a function ofpitch, the target features are less dependent upon reticle error.Furthermore, the FOCAL data (focus vs. overlay error) must be calibratedfor every point in the exposure field similar to phase-shift monitors(typically at 121 points across an exposure field, see FIG. 10). Now, itis possible to use FOCAL to separate out lens tilt and astigmatism fromdynamic FPD maps and provide a dynamic focal plane map, but wafer heightvariation and stage synchronization errors would still be included inthe result. See, for example, “193 Step and Scan Lithography”, supra;and “Comprehensive Focus-Overlay-CD Correlation to IdentifyPhotolithographic Performance”, supra.

Schnitzl Targets: A method described by Ausschnitt in “DistinguishingDose from Defocus for In-Line Lithography Control”, C. Ausschnitt, SPIE,Vol. 3677, pp. 140-147, 1999, makes use of line-end shortening effectsto decouple focus drift from exposure drift on semiconductor productwafers. FIG. 9 shows a typical pair of Schnitzl targets (focusingfiducials). It is widely known that resist line-ends (FIG. 9) are verysensitive (exhibit greater line-end shortening) to both focus andexposure drifts; the effect is further enhanced as the lithographicprocess is pushed near performance limit of the scanner tool (˜λ/2NA).Using the Schnitzl targets and a fairly elaborate method of calibration(CD-SEM measurements and a coupled system of equations) Ausschnittoffers a method that can determine the magnitude of focus drift onproduct wafers using one or more exposures in the presence of exposuredrift (see FIG. 10 for example results). Since changes in focus andexposure can produce similar changes in the critical dimension (CD) theSchnitzl method is useful for day-to-day process monitoring because iteliminates the need to constantly perform focus and exposure experiments(FEM—a Focus Exposure Matrix) in-between production runs. In addition,the method uses fast and accurate optical overlay tools to measure theSchnitzl patterns (in several forms, CD targets or Overlay targets,FIGS. 8-9) after wafer processing, this saves monitoring costs becauseoptical overlay tools are less expensive to operate as compared with aCD-SEM. While decoupling focus drift from exposure drift is useful forprocess monitoring, the method in its present form requires twoexposures at different focus settings to determine the absolute focaldrift (direction). Performing extra exposures during production runs isvery costly. In addition, since the initial Schnitzl target calibrationprocedure depends on a number of lithographic tool settings (line size,pitch, sigma, NA) re-calibration is required for each lithographicprocess change—including changes in metrology tools. The Schnitzlfocusing fiducials are often used to map out FPD across a stepper orscanner field, but methods similar to those described in “Comprehensivefocus-overlay-CD correction to identify photolithographic performance”,Dusa, et al., SPIE Vol. 2726-29, 1996, would need to be implemented toobtain a dynamic focus map—but again, wafer height variation andscanning dynamics are not considered.

SUMMARIZING

Several methods for determining FPD have been described. Common to allof these methods is that a feature (focusing fiducial or FF) is printedon a wafer and the focusing fiducial is subsequently measured. The datafrom the focusing fiducial is processed and an FPD value, δZ, isdetermined. Further, and common to all these methods, the contributionsof wafer height, lens aberrations (in the form of lens field curvature),and stage synchronization are not resolved into their distinctcomponents.

SUMMARY

In accordance with the present invention, a process for the properdetermination of SFPD in the presence of wafer height variation, ZW(x,y), is described.

A series of lithographic exposures is performed on a resist coatedsilicon wafer using a photolithographic scanner. The lithographicexposures produce an array of focusing fiducials that are displacedrelative to each other in a unique way. The focusing fiducials aremeasured and the FPD computed. The resulting measurements are fed into acomputer algorithm that calculates the dynamic scanning field curvaturein an absolute sense in the presence of wafer height variation and otherwafer/reticle stage irregularities. Alternative embodiments of thepreferred embodiment allow for the determination of dynamic scanningfield curvature for scanning systems with asymmetric exposure fields.

Other features and advantages of the present invention should beapparent from the following description of the preferred embodiment,which illustrates, by way of example, the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of this invention believed to be novel and the elementscharacteristic of the invention are set forth with particularity in theappended claims. The figures are for illustration purposes only and arenot drawn to scale. The invention itself, however, both as toorganization and method of operation, may best be understood byreference to the detailed description which follows taken in conjunctionthe accompanying drawings in which:

FIG. 1 shows photolithographic scanner system.

FIG. 2 shows typical dynamic lens field curvature plot with zero moment.

FIG. 3 shows wafer flatness correctables and high order terms.

FIG. 4 shows the scanner exposure field coordinate system.

FIG. 5 shows focus error components for the scanner, wafer, and lens.

FIG. 6 shows scanner tilt definitions.

FIG. 7 generic wafer/stage leveling system with detector and source.

FIG. 8 shows typical focusing fiducials for; FOCAL, PSFM, and Schnitzlmethods.

FIG. 9 shows typical focusing fiducials (FF) for FOCAL, PSFM, andSchnitzl.

FIG. 10 shows a PSFM and Schnitzl calibration plot for one field point.

FIG. 11 shows the process flow for the first Main Embodiment.

FIG. 12 shows a reticle with multiple focusing fiducials.

FIG. 13 shows wafer with wafer alignment marks (180° and 270°).

FIG. 14 a shows the exposure pattern after the first exposure of thefirst Main Embodiment.

FIG. 14 b shows a schematic of the exposed field after the 2^(nd)exposure of the first Main Embodiment.

FIG. 15 shows schematic of focusing fiducial reticle used to carryoutexposures shown in FIGS. 14 a and 14 b.

FIGS. 16 and 17 show output for the system of FIG. 1, providing scanningfield curvature and wafer height error data map.

FIG. 18 shows the steps for carrying out the second Main Embodiment.

FIG. 19 shows in schematic the sections of the FF reticle used for thesecond Main Embodiment as illustrated in FIGS. 20, 21 and 22.

FIG. 20 shows a schematic of the first exposure for an NX=5 by NY=7array of focusing fiducials.

FIG. 21 shows a schematic of the exposed field after the 2^(nd) exposurefor the second Main Embodiment.

FIG. 22 shows a schematic of the exposed field after the 3^(rd) exposurefor the 2^(nd) main embodiment.

FIG. 23 shows the relation of the wafer coordinates, wafer notch angleand lithography tool scanning direction to one another.

FIG. 24 is a block diagram illustrating a technique for processing thefinal output.

FIG. 25 is a block diagram illustrating another technique for processingthe final output.

DETAILED DESCRIPTION

Dynamic Focal Plane Deviation

It is desired to determine the performance of Scanner dynamic FocalPlane Deviation (SFPD) resulting from the imperfect synchronization ofthe wafer and reticle stages due to their mutual motion in the Zdirection as the scanner operates. FIG. 1 is a schematic diagram of ascanner system constructed in accordance with the invention. FIG. 1shows a scanner and motion of the reticle (ΔZ ret) and wafer (ΔZ waf)perpendicular to the scanning direction as responsible for what shall bereferred to as “dynamic scanning field curvature” or “dynamic scan FPD”or simply “SFPD”. The SFPD is the deviation in net focus at the waferplane that is attributable to the wafer height sensors and adjusters,independent from other dynamic focal errors such as dynamic lens fieldcurvature, reticle/wafer stage irregularity (bow and warp), and waferheight variations. Thus, the invention is directed to a process for theproper determination of SFPD in the presence of wafer height variation,ZW(x, y).

The term δZ (x, y) is defined as the net focal deviation or focal planedeviation (FPD) at a wafer plane located at (x, y). This can bedetermined a variety of ways, as described below. We can decompose SZ(x,y) into contributions from the lens, the scan, and the wafer as:δZ(x,y)=ZL(x)+ZS(y)+x*θ(y)+ZW(x,y)  (Equation 1)where we use a continuous field position (x, y) and:

-   -   ZL(x)=dynamic lens field curvature=contribution from lens. This        is typically known to within an overall piston and roll (a+b*x,        where; a and b are constant). See FIGS. 2 and 5.    -   ZS(y)=dynamic scan piston. As discussed in “Dynamic Lens Field        Curvature” supra, this is the moving average of a combination of        instantaneous piston and pitch. See FIG. 5.    -   θ(y)=dynamic scan roll. This is a moving average of        instantaneous scanner roll. See FIGS. 5 and 6.    -   ZW(x, y)=wafer height variation over the scan field. See FIGS. 3        and 5.        In addition; as described below, we define ZS(y) and θ(y) as the        scanner dynamic focal plane deviation (SFPD). This is simply the        scanner field curvature error associated with stage        synchronization error in the Z direction. It should be noted        that, even if there is a perfect lens with no dynamic lens field        curvature (ZL=0), there can still be focal plane deviation due        to SFPD (ZS and θ≠0).

Thus, a process for the determination of dynamic scanning fieldcurvature uniquely associated with a photolithographic scanner isprovided. A series of lithographic exposures is performed on a resistcoated silicon wafer using a photolithographic scanner. The lithographicexposures produce an array of focusing fiducials that are displacedrelative to each other in a unique way. The focusing fiducials aremeasured using an optical metrology tool. The resulting measurements arefed into a computer algorithm that calculates the dynamic scanning fieldcurvature or dynamic scan focal plane deviation (SFPD) in an absolutesense in the presence of wafer height variation and other wafer/reticlestage irregularities.

Several different embodiments of systems constructed in accordance withthe invention will be described. For purposes of discussion, each ofthese will be referred to as “main embodiments”, although it should benoted that the embodiments comprise alternative constructions of systemsthat implement the teachings described herein.

Discussion of First Main Embodiment

In accordance with the invention, Focusing Fiducials (FF) are exposedonto a wafer in such a manner that the effects of wafer heightvariations can be isolated and eliminated, and a true measure of dynamicscan FPD (SFPD) can be obtained.

A process flow diagram for the first Main Embodiment is shown in FIG.11. A schematic of a reticle containing a (2 m×+1*2my+1) array offocusing fiducials is shown in FIG. 12. Details for the first MainEmbodiment will be explained for a square exposure field (m×=my)although it is appreciated that the case of rectangular fields is adirect generalization from that description.

1. Provide Wafer

A resist coated wafer with wafer alignment marks disposed at 180° and270° is provided (FIG. 13). The purpose of marks is to allow wafer to beinserted and aligned at two distinct notch angles that differ by +90° or−90° from one another. Depending on the scanner and FPD technologyapplied, the wafer notch itself could provide sufficient accuracy forthe subsequent wafer alignments.

2. Load and Align Wafer

A wafer is then loaded at a notch angle N(N=0°, 90°, 180° or 270°) andis aligned to the corresponding wafer alignment marks.

3. Provide, Load and Align Reticle

A focusing fiducial reticle is provided. The exact form taken depends onthe technology employed, but they are all schematically represented inFIG. 12 as a (2 m×+1)* (2my+1) array of focusing fiducials (FF) on apitch or spacing equal to P. The size or extent of each individual FF isS. The reticle is loaded and aligned on the scanner. FIG. 15 is aschematic of an exemplary focusing fiducial reticle that can be used inthis embodiment.

4. First Exposure

A reticle (R) containing an array of focusing fiducials (FF) at2mx+1*2my+1 sites (FIG. 12) is exposed onto the wafer—forming exposurefield, A (FIG. 14 a, with m×=2, my=2 for example), where the projectionof the individual focusing fiducial field points are labeled by theunprimed letters A:Y. In the following, we discuss the case where Nx andNy are odd numbers, Nx=2 m×+1, Ny=2my+1. The foregoing can be readilygeneralized to mixed odd-even, even-odd and even-even (NX−NY)configurations. This exposure is done with the field centered atposition (XW1, YW1) on the wafer. A schematic of the exposed field isshown in FIG. 14 a. Focusing Fiducials, FF, are indicated by the squareboxes and labeled A: Y. Indices i and j indicating position within thescanned field of$\left\lbrack {{{XF}(i)},{{YF}(j)}} \right\rbrack = \left( {{i*\frac{P}{M}},{j*\frac{P}{M}}} \right)$are also shown. (XF, YF) are the coordinates (x, y) shown in FIG. 4.

5. Rotate Wafer and Align

The wafer is next rotated to a desired angle, for example the wafer canbe rotated to notch angle 90° different from the original notch angle N(i.e. N±90°). It is aligned to the corresponding wafer alignment marks.

6. Second Exposure

The wafer is now exposed with field center shifted a distance G from thefirst exposure. FIG. 14 b shows the field after the second exposure.Focusing Fiducials A′: Y′ were put down by this second exposure. Theoffset G is chosen so the focusing fiducials remain distinct and useablebut the wafer flatness does not vary significantly over an interval ofthe size G. Since G is typically <1 mm at the wafer, only the higherfrequency spatial variations contribute. Since the power spectraldensity of wafer flatness falls off rapidly at higher spatialfrequencies, the variation over sizes <1 mm will typically be small (≦10nm). In FIG. 14 b, the wafer was rotated −90° from the original notchangle position for that exposure.

7. Develop Wafer

The wafer is now (optionally) developed. In the case of technologiesthat utilize the latent image, this step may be omitted. See, forexample, “FOCAL: Latent Image Metrology for Production Wafer Steppers”,supra. Also, after development, the wafer may be etched and thephotoresist stripped to improve the quality of the focusing fiducials.

8. Measure Focus Fiducials

At this point, the focusing fiducials are measured and the dataconverted to an FPD value δZ. For example, if each FF was a box-in-boxarray exposed using a large pinhole aperture plate as described in U.S.Pat. No. 5,828,455, supra, and U.S. Pat. No. 5,978,085, supra, thenafter measuring each box-in-box array, we could determine the Zernikecoefficient a4 and thereby infer the FPD: $\begin{matrix}{{\delta\quad Z} = {\frac{\mathbb{d}z}{{\mathbb{d}a}\quad 4}a\quad 4}} & \left( {{Equation}\quad 2} \right)\end{matrix}$See, for example, “Gauging the Performance of an In-SituInterferometer”, M. Terry et al. Denote the notch angle N focusingfiducial FPD values as:δZ_(ij)  (Equation 3)where i=−mx:mx and j=−my:my. In FIG. 14 b, these are the FPD valuescorresponding to FF's A:Y. Likewise, the FPD values corresponding to theFF's of the second exposure are:δZ90_(ij)  (Equation 4)where i, j run over the same indices. In FIG. 14 b, these are the FPDvalues corresponding to FF's A′:Y′. Now, we can decompose δZ(x,y) intocontributions from the lens, the scan and the wafer as in Equation 1.δZ(x,y)=ZL(x)+ZS(y)+x*θ(y)+ZW(x,y)  (Equation 5)This decomposition will be utilized below.

9. Provide Dynamic Field Curvature

Now while the dynamic lens field curvature, ZL(x), contributes to theFPD measurement, δZ, it must be excluded from assessment of the scannerheight sensor/actuator subsystem. To take an extreme case, a flat wafer(ZW=0) and perfect scan hardware (ZS=q=0) would still exhibit a non-zeroFF measurement δZ, since:δZ(x,y)=ZL(x)  (Equation 6)Since ZL(x) is independent of scanner dynamics, it can be determinedonce and subsequently subtracted from many δZ(x, y) data sets on asingle scanner. For example, ZL(x) can be determined using a techniqueas described in co-pending application entitled “APPARATUS AND PROCESSFOR DETERMINATION OF DYNAMIC LENS FIELD CURVATURE” by Smith et. al,application Serial Number, (Attorney Docket Number 38203-6090), assignedto the assignee of the present application. Also, as mentioned above,ZL(x) will typically not be determined to within a function a+b*x, wherea and b, like ZL(x), will be independent of scan dynamics. In this case,the ZL(x) used in Equation 5 will have average and first moment=0 (FIG.2). $\begin{matrix}{{\int_{- \frac{sw}{2}}^{\frac{sw}{2}}{\frac{\mathbb{d}x}{SW}{{ZL}(x)}}} = {0\quad{and}}} & \left( {{Equation}\quad 7} \right) \\{{\int_{- \frac{sw}{2}}^{\frac{sw}{2}}{\frac{\mathbb{d}x}{SW} \times {{ZL}(x)}}} = 0} & \left( {{Equation}\quad 8} \right)\end{matrix}$where; SW is the slot width or width of the optical projection fieldperpendicular to the scan direction (FIG. 4). So, we are provided withthe scanner dynamic field curvature ZL(x). The preferred method fordetermining the provided ZL(x) is described in the “APPARATUS ANDPROCESS FOR DETERMINATION OF DYNAMIC LENS FIELD CURVATURE” patentapplication, supra.

10. Determine Dynamic Focal Plane Deviation

At this point, we combine the measured FPD values δZ_(ij), δZ90_(ij) andthe provided dynamic lens field curvature δZL_(i) to determine thescanning focal plane deviation, SFPD, (ZS_(j), θ_(j)) and wafer heightdeviation ZW_(ij).

Referring to FIG. 14 b, and using the discrete indices i and j, weexpress δZ_(ij) and δZ90_(ij) as: $\begin{matrix}{{\delta\quad Z_{ij}} = {{ZL}_{i} + {ZW}_{ij} + {ZS}_{j} + {i*\frac{P}{M}\theta_{j}}}} & \left( {{Equation}\quad 9} \right) \\{{\delta\quad Z\quad 90_{ij}} = {{ZL}_{j} + {ZW}_{ij} + {{ZS}\quad 90_{i}} + {j*\frac{P}{M}{\theta 90}_{i}}}} & \left( {{Equation}\quad 10} \right)\end{matrix}$where:

-   -   ZS90_(i),θ90_(i)=analogs of ZS_(j), θ_(i) for the scan done at        90° rotation.    -   P=pitch of FF's on reticle    -   M=projection tool reduction magnification (=4 typically) and the        other symbols are as previously defined.

Because ZL is known, it can subtract it from both sides of Equations 9and 10 and defining M_(ij) and M90_(ij), $\begin{matrix}{M_{ij} = {{{\delta\quad Z_{ij}} - {ZL}_{i}} = {{ZW}_{ij} + {ZS}_{j} + {i*\frac{P}{M}\theta_{j}}}}} & \left( {{Equation}\quad 11} \right) \\{{M\quad 90_{ij}} = {{{\delta\quad{Z90}_{ij}} - {ZL}_{j}} = {{ZW}_{ij} + {{ZS}\quad 90_{j}} + {j*\frac{P}{M}{\theta 90}\quad i}}}} & \left( {{Equation}\quad 12} \right)\end{matrix}$

Both M_(ij) and M90_(ij) are known from our knowledge of δZ_(ij),δZ90_(ij) and ZL_(i). Equations 11 and 12 can now be solved for ZW_(ij),ZS_(j), θ_(j), ZS90_(i), and θ90_(i) via the singular valvedecomposition but not without ambiguity. As discussed further below,these ambiguities can be resolved. See “Numerical Recipes, The Art ofScientific Computing”, W. Press et al., Cambridge University Press, pp.52-64, 1990; and “Numerical Recipes, The Art of Scientific Computing”,W. Press et al., Cambridge University Press, pp. 509-520, 1990. It canbe shown that Equations 11 and 12 imply: $\begin{matrix}{{ZW}_{ij} = {{ZW}_{ij}^{\prime} + c^{''} + {d^{''}*j} + {e^{''}*i} + {f^{''}*i*j}}} & \left( {{Equation}\quad 13} \right) \\{{ZS}_{j} = {{ZS}_{j}^{\prime} + c + {d*j}}} & \left( {{Equation}\quad 14} \right) \\{{\frac{P}{M} \cdot \theta_{j}} = {{\frac{P}{M}\theta_{j}^{\prime}} + e + {f*j}}} & \left( {{Equation}\quad 15} \right) \\{{{ZS}\quad 90_{i}} = {{{ZS}\quad 90_{i}^{\prime}} + c + {e*i}}} & \left( {{Equation}\quad 16} \right) \\{{\frac{P}{M}\theta\quad 90_{i}} = {{\frac{P}{M}\theta\quad 90_{i}^{\prime}} + d + {f*i}}} & \left( {{Equation}\quad 17} \right)\end{matrix}$where the single primed quantities (ZW′_(ij), ZS′_(j), θ_(j)′, . . . )are uniquely determined but the constants c, c″, d, d″, e, e″, f, f″ areonly partially determined. The relations amongst the remaining unknownquantities are:c1=c+c″  (Equation 18)d1=d+d″  (Equation 19)e1=e+e″  (Equation 20)f1=f+f″  (Equation 21)where c1, d1, e1, f1 are determined from the M_(ij), M90_(ij) and thesingle primed quantities (ZW′_(ij), . . . ). We now discuss theresolution of these ambiguities.c+c″

From Equation 14, c represents the average piston or average offset ofthe SFPD while c″ (Equation 13) is the average wafer height over thescanning field. While we know their combination (Equation 18), Equations11 and 12 do not specify their apportionment.

However, since average wafer height over the scan field should becorrected or compensated for by the scanner height sensors andactuators, we can assign all of this deviation to the scanner.

By this interpretation we then have:c″=0  (Equation 22)c=c1  (Equation 23)d+d″

From Equation 14, d represents the average slope of the dynamic scanpiston ZS_(j) while d″ in Equation 13 is the average wafer slope in thescan direction. Again, we know the value of their sum, d1 of Equation19, but Equations 11 and 12 provide no more information.

In this case, average wafer slope, d″, should be completely correctibleby the scanning height sensors and actuators. The combination d+d″represent the error in correcting for average wafer height. Therefore bythis interpretation we have:d″=0  (Equation 24)d=d1  (Equation 25)e+e″

This combination consists of wafer tilt in the y-direction (e″ inEquation 13) and dynamic scan piston (Z90_(i), Equation 16) slope. Itsresolution is similar to the d+d″ case. There results:e″=0  (Equation 26)e=e1  (Equation 27)f+f″

f″ in Equation 13 is 45° rotated, saddle shaped wafer height variationover exposure field. Because of its long range character, this modeshould be well detected with high fidelity by the scanner look aheadsensors.

f*i*j=i*(f*j)=linearly varying roll (θ_(j)) over the wafer field(linearly varying pitch across the field is not possible physically).This scanner mode can be reconstructed by linearly increasing theinstantaneous roll (as opposed to the slot height averaged roll, θ_(j))linearly in time at constant scan speed.

The combination, (f+f′)*i*j represents the total error of the scannersystem in correcting for 45° saddle wafer height deviations. So whilethe relative contributions of the wafer and scanner are not determined,we do know the scanner error or bias in this mode. Since it is a 100%correctable mode, we can justifiably attribute all of it to theperformance of the scanner height sensors and adjusters.

So:f″=0  (Equation 28)f=f1  (Equation 29)Algorithm

At this point, we have uniquely determined the SFPD for both scans((ZS_(j), θ_(j)), (ZS90_(j), θ90_(j))).

The method for doing so consisted of subtracting out the provided lensdynamic field curvature from the measured FPD values and solving theresulting equations (11 and 12) using the minimum norm solution providedby the singular value decomposition. See, for example, “NumericalRecipes, The Art of Scientific Computing”, pp. 52-64, supra, “NumericalRecipes, The Art of Scientific Computing”, pp. 509-520, supra. CallingZW*_(ij) the numerical solution for ZW_(ij) from this process wecalculate the constants c″, d″, e″, f″ which minimize: $\begin{matrix}{E = {\sum\limits_{i,j}\left\lbrack {{ZW}_{ij}^{*} - \left( {c^{''} + {d^{''}*j} + {e^{''}*i} + {f^{''}*i*j}} \right)} \right\rbrack^{2}}} & \left( {{Equation}\quad 30} \right)\end{matrix}$

This is easily done by least squares techniques well-known to thoseskilled in the art. Then we compute ZW_(ij), ZS_(j), θ_(j),Z90_(i),θ90_(i) as: $\begin{matrix}{{ZW}_{ij} = {{ZW}_{ij}^{*} - \left( {c^{''} + {d^{''}*j} + {e^{''}*i} + {f^{''}*i*j}} \right)}} & \left( {{Equation}\quad 31} \right) \\{{ZS}_{j} = {{ZS}_{j}^{*} + c^{''} + {d^{''}*j}}} & \left( {{Equation}\quad 32} \right) \\{{\frac{P}{M}\theta_{j}} = {{\frac{P}{M}\theta_{j}^{*}} + e^{''} + {f^{''}*i}}} & \left( {{Equation}\quad 33} \right) \\{{{ZS}\quad 90_{i}} = {{{ZS}\quad 90^{*}} = {c^{''} + {e^{''}*i}}}} & \left( {{Equation}\quad 34} \right) \\{{\frac{P}{M}\theta\quad 90_{i}} = {{\frac{P}{M}{\theta 90}_{i}^{*}} + d^{''} + {f^{''}*i}}} & \left( {{Equation}\quad 35} \right)\end{matrix}$Where the starred (*) quantities are the minimum norm SVD solutions, andZW_(ij), (ZS_(j), θ_(j)), (ZS90_(i), θ90_(i)) represents our finaldetermination of wafer flatness and SFPD. FIGS. 16 and 17 show examplesof the final results of the method described above.

Discussion of Second Main Embodiment

In the first Main Embodiment we have discussed in detail the practice ofthis invention to cases where the size of the scanned field (FX, FY)(FIG. 4) is smaller than or equal to the lesser of the slot width SW andmaximum scan length SL. The present embodiment is practiced when FY (theinterrogated field size in the Y direction) is greater than the maximumslot width, SW of FIG. 4. In terms of the focusing fiducials on thefocusing fiducial reticle of FIG. 12, if we call the maximum number ofFF's across the projected field in the X or cross scan directionNX_(max) and the required number of FF's in the Y or scan direction NY,whenNX _(max) <NY<2NX _(max)−1  (Equation 36)we can apply the present embodiment. Equation 36 typically holds forscanner fields. FIG. 18 outlines the steps for carrying out the presentembodiment.

Provide Wafer, Load and Align Wafer

The first two operations for the second Main Embodiment (listed as“provide wafer” and “load and align wafer”) are the same as thecorresponding operations in the first Main Embodiment described above.The first and second Main Embodiment differs in the subsequentoperations:

Provide, Load, and Align Reticle

FF reticle as above is provided, loaded, and aligned. FIG. 19 shows thesections of this FF reticle used to carry out the exposures illustratedin FIGS. 20, 21, and 22. FF's are indicated by squares and have eachbeen distinctly labeled with the letters A:AI.

First Exposure

An NX×NY array of focusing fiducials is exposed. As discussed above,NX_(max)<NY. FIG. 20 shows an NX=5×NY=7 first exposure with FF'srepresented by squares labeled A:AI. This exposure was made with wafernotch angle (N)=270°.

Rotate Wafer

The wafer is now rotated a desired angle, for example the wafer may berotated −90° so the orientation of the wafer relative to the scanningdirection will be as shown in FIG. 23, ‘Notch angle=180°’.

Second Exposure

An NX×NX exposure slightly offset a distance G from the first exposureis now done. It overlaps rows irow=1:NX and columns icol=1:NX of thefirst exposure. FIG. 21 shows the result at overlapping exposures. A′:Y′are the FF's exposed during this step, the scan direction is indicatedby the double pointed arrow. Note that rows irow=6:7 are not overlappedduring this exposure.

Shift Wafer

The wafer is now shifted and slightly offset so that the non-overlappedrows irow=NX+1:NY (irow=6:7 of FIG. 21) are overlapped with the two rowsof the original exposure irow=NX−1: NX (irow=4:5 of FIG. 20) followingrotation of the wafer.

Third Exposure

The wafer is now exposed so the non-overlapped rows irow=NX+1:NY(irow=6:7 of FIG. 21) are overlapped with and the two rows of theoriginal exposure irow=NX−1: NX (irow=4:5 of FIG. 20). In FIG. 22corresponding sites on the FF reticle of FIG. 19 are indicated by thesame letter e.g. A, A′, and A″ of FIG. 22 are FF's exposed using the FFlabeled A in FIG. 19. The purpose of the two overlapped rows (irow=4:5)is to ‘stitch together’ in the Z direction the second and third scans.Separate scans must have two or more rows overlapped for this inventionto be operable.

Develop Wafer

The wafer is now (optionally) developed. In the case of technologies(See, for example, “FOCAL; Latent Image Metrology for Production WaferSteppers”, supra) that utilize the latent image, this step may beomitted. Also, after development, the wafer may be etched and thephotoresist stripped to improve the quality of the focusing fiducials.

Measure Focus Fiducials

The focusing fiducials are now measured and converted to FPD values.From the first exposure (FF's A: AI of FIG. 22) we set the FPD valuesδZ_(ij)  (Equation 37)

-   -   i=−mx:mx, j=−my:my        where    -   NX=2mx+1 and NY=2my+1.        In the case of FIG. 22 we have m×=2, my=3.

From the second exposure (FF's A′:Y′ of FIG. 22) we get the FPD valuesδZL90_(ij)  (Equation 38)

-   -   i=−mx:mx, j=−my:2mx−my        From the third exposure (the double primed (″) FF's in FIG. 22)        we get the FPD values        δZL90_(ij)  (Equation 39).    -   i=−mx:mx, j=2mx−my−1:my

In Equations 37, 38 and 39 we have indexed the FPD values by the i, jindex corresponding to its physical column, row position within theexposure field.

Provide Dynamic Field Curvature

Now while the dynamic lens field curvature, ZL(x), contributes to theFPD measurement, δZ, it must be excluded from assessment of the scannerheight sensor/actuator subsystem.

So, we are provided with the scanner dynamic field curvature ZL(x).“Dynamic Lens Field Curvature”, supra describes the preferred method fordetermining ZL.

Determine Dynamic Focal Plane Deviation

At this point, we combine the measured FPD values δZ_(ij), δZL90_(ij),δZU90_(ij) and the provided dynamic lens field curvature ZL_(i) todetermine the SFPD (ZS_(j), θ_(j)) of the first scan and the waferheight deviation, ZW_(ij), at the FF's.

We now express the measured FPD values as in Equations 9 and 10 by thefollowing equation systems: $\begin{matrix}\left. \begin{matrix}{{\delta\quad Z_{ij}} = {{ZL}_{i} + {ZW}_{ij} + {ZS}_{j} + {i*\frac{P}{M}\theta\quad j}}} \\{i = {{{- {mx}}\text{:}{mx}\quad j} = {{- {my}}\text{:}{my}}}}\end{matrix} \right\} & \left( {{Equation}\quad 40} \right) \\\left. \begin{matrix}{{\delta\quad Z\quad L\quad 90_{ij}} = {{ZL}_{j + {KLI}} + {ZW}_{ij} + {{ZSL}\quad 90_{i}} + {\left( {j + {KL}} \right)\frac{P}{M}\theta\quad L\quad 90_{i}}}} \\{i = {{{- {mx}}\text{:}{mx}\quad j} = {{{{- {my}}\text{:}2{mx}} - {{my}\quad{KL}}} = {{KLI} = {{my} - {mx}}}}}}\end{matrix} \right\} & \left( {{Equation}\quad 41} \right) \\\left. \begin{matrix}{{\delta\quad{ZU}\quad 90_{ij}} = {{ZL}_{j + {KUI}} + {ZW}_{ij} + {{ZSU}\quad 90_{i}} + {\left( {j + {KU}} \right)\frac{P}{M}\theta\quad U\quad 90_{i}}}} \\{i = {{{- {mx}}\text{:}{mx}\quad j} = {{2{mx}} - {my} - {1\text{:}{my}}}}} \\{{KUI} = {{{{- 3}{mx}} + {my} + {1\quad{KU}}} = {\frac{1}{2} - {mx}}}}\end{matrix} \right\} & \left( {{Equation}\quad 42} \right)\end{matrix}$where:

-   -   (ZS_(j), θ_(j))=(integrated scanner piston/pitch, integrated        scanner roll) for the first exposure    -   (ZSL90_(i), θL90_(i))=similar for second exposure    -   (ZSU90_(i), θU90_(j))=similar for third exposure    -   P=pitch of FF's on reticle    -   M=projection tool reduction magnification ratio and the other        symbols are as previously defined.

As before, we subtract the provided ZL from both sides of Equations 40,41 and 42 to get: $\begin{matrix}\left. \begin{matrix}{M_{ij} = {{{\delta\quad Z_{ij}} - {ZL}_{i}} = {{ZW}_{ij} + {zs}_{j} + {i*\frac{P}{M}\theta_{j}}}}} \\{i = {{{- {mx}}\text{:}{my}\quad j} = {{- {my}}\text{:}{my}}}}\end{matrix} \right\} & \left( {{Equation}\quad 43} \right) \\\left. \begin{matrix}{{M\quad L\quad 90_{ij}} = {{{{\delta Z}\quad L\quad 90_{ij}} - {ZL}_{j + {KLI}}} = {{ZW}_{ij} + {{ZSL}\quad 90_{i}} + {\left( {j + {KL}} \right)\frac{P}{M}\theta\quad L\quad 90_{i}}}}} \\{i = {{{- {mx}}\text{:}{mx}\quad j} = {{{{- {my}}\text{:}2{mx}} - {{my}\quad{KL}}} = {{KLI} = {{my} - {mx}}}}}}\end{matrix} \right\} & \left( {{Equation}\quad 44} \right) \\\left. \begin{matrix}{{{MU}\quad 90_{ij}} = {{{{\delta Z}\quad U\quad 90_{ij}} - {ZL}_{j + {KUI}}} = {{ZW}_{ij} + {{ZSU}\quad 90_{i}} + {\left( {j + {KU}} \right)\frac{P}{M}\theta\quad{U90}_{i}}}}} \\{i = {{{- {mx}}\text{:}{mx}\quad j} = {{{2{mx}} - {my} - {1\text{:}{my}\quad{KUI}}} = {{{- 3}{mx}} + {my} + 1}}}} \\{\quad{{KU} = {\frac{1}{2} - {mx}}}}\end{matrix} \right\} & \left( {{Equation}\quad 45} \right)\end{matrix}$

The equation system represented by Equations 43, 44 and 45 can now besolved for ZW_(ij), ZS_(j), θ_(j), ZSL90_(i), θL90_(i), ZSU90_(i), andθU90_(i) by the singular value decomposition. See, for example,“Numerical Recipes, The Art of Scientific Computing”, pp. 52-64, supra;and “Numerical Recipes, The Art of Scientific Computing”, pp. 509-520,supra. However, the solution is not unique as these are four singular orundetermined modes to the system of equations. An investigation intotheir structure reveals that they can all be associated with anambiguity in the wafer heights ZW_(ij) of the formZW _(ij) =ZW′ _(ij) +c″+d″*j+e″*i+f″*i*j  (Equation 46)

-   -   i=−mx:mx, j=−my:my        and an ambiguity in the first exposure SFPD that takes the form:        $\begin{matrix}        {{ZS}_{j} = {{ZS}_{j}^{\prime} + c + {d*j}}} & \left( {{Equation}\quad 47} \right) \\        {{\frac{P}{M}\theta_{j}} = {{\frac{P}{M}\theta_{j}^{\prime}} + e + {f*j}}} & \left( {{Equation}\quad 48} \right)        \end{matrix}$        The second and third exposure SFPD's also exhibit an ambiguity        that is a function of the parameters (c, c″, d, d″, e, e″, f,        f″) but involves no new parameters. The discussion of the        resolution of these ambiguities is now the same as in the first        Main Embodiment and we can proceed with the algorithm for        determining SFPD.        Algorithm

The technique for determining the SFPD for the first scan (ZS_(j),θ_(j)) and the wafer heights at the FF locations consists of thefollowing operations:

-   -   Subtract out the provided lens dynamic field curvature (ZL) from        the measured FPD's (δZ) per Equations 43, 44 and 45;    -   Solve Equations 43, 44, and 45 using the minimum norm singular        value decomposition to arrive at a numerical solutions for the        wafer heights (ZW*_(ij)), the first scan SFPD (ZS*_(j), θ*_(j))        and the second and third scan SFPD (see “Numerical Recipes, The        Art of Scientific Computing”, pp. 52-64, supra and “Numerical        Recipes, The Art of Scientific Computing”, pp. 509-520, supra);    -   Minimize the quantity $\begin{matrix}        {E = {\sum\limits_{i,j}\left\lbrack {{ZW}_{ij}^{*} - \left( {c^{''} + {d^{''}*j} + {e^{''}*i} + {f^{''}*i*j}} \right)} \right\rbrack^{2}}} & \left( {{Equation}\quad 49} \right)        \end{matrix}$    -    over the quantities c″, d″, e″, f″ and thereby determine their        values;    -   Compute the SFPD of the first scan as: $\begin{matrix}        {{ZS}_{j} = {{ZS}_{j}^{*} + c^{''} + {d^{''}*j}}} & \left( {{Equation}\quad 50} \right) \\        {{\frac{P}{M}\theta_{j}} = {{\frac{P}{M}\theta_{j}^{*}} + e^{''} + {f^{''}*j}}} & \left( {{Equation}\quad 51} \right)        \end{matrix}$    -   Compute the wafer height variation at the FF's as:        ZW _(ij) =ZW _(ij)*−(c″+d″*j+e″*i+f″*i*j)  (Equation 52)        FIGS. 16 and 17 show the final results of the method of this        embodiment.

Variations of the Main Embodiments

We now outline a number of variations of the two main embodiments ofthis invention.

In the second Main Embodiment, we discussed and showed in detail thecase of the minimum overlap (2 rows) required by the second and thirdexposures. Improved performance results by overlapping more than tworows, measuring the complete set of FF's, setting up the equationsanalogous to Equations 43, 44, and 45 and then carrying out the steps inthe algorithm section.

An extension of the second Main Embodiment would consist of threeadditional exposures done at −90° to the first exposure, each additionalexposure overlapping at least two rows of the adjacent exposures. Fourequation sets instead of three sets (Equations 43, 44, and 45) are setup, solved and the ambiguity resolved as in the second Main Embodiment.

Four or more additional exposures at −90° from the first exposure isanother variation on the second Main Embodiment.

Heretofore in our exposition of the two main embodiments, we havereferred to single exposures of the scanner as creating the necessaryFF's on the wafer. Some technologies such as PSFM will produce FF's in asingle exposure. See, for example, U.S. Pat. No. 5,300,786, supra.Technologies such as the In-Situ Interferometer require two separateexposures to create a single focusing fiducial. One exposure creates theso-called ‘MA’ pattern that is the carrier of the wafer, lens andscanner height variation information, while the other exposure createsthe so-called ‘MO’ pattern. See U.S. Pat. No. 5,828,455, supra; and U.S.Pat. No. 5,978,085, supra. The MO pattern creates a reference so theresulting FF can be read in an overlay metrology tool. Since the MO doesnot carry any significant wafer lens or scanner height variationinformation, this second exposure, for the purposes of this invention,can be lumped together with the first or MA exposure.

The process described above could be made more sophisticated and preciseby taking into account reticle flatness effects. If we previouslymeasure or otherwise know the reticle flatness and then provide it(ZR_(ij)) then referring the Equations 11 and 12, we would computeM_(ij) and M90_(ij) as:M _(ij) =δZ _(ij) −ZL _(i) −ZR _(ij) /M ²  (Equation 53)M90_(ij) =δZ90_(ij) −ZL _(j) −ZR _(i j-1) /M ²  (Equation 54)where

-   -   ZR_(ij)=reticle flatness deviation at x location=i and y        location=j (FIG. 12)    -   M=reduction magnification ratio (typically 4).

The subsequent steps of the first Main Embodiment then follow word forword. Technique applies to the second Main Embodiment andgeneralizations of same.

Therefore, in the case of ISI technology being used for creating FF's,we would call the MA/MO exposure pair an exposure group. Then, inapplying the two main embodiments to an ISI FF, the called for‘exposures’ would be replaced by ‘exposure groups’, each exposure groupconsisting of an MA/MO pair made in accordance with the practice of theISI FF technology. See U.S. Pat. No. 5,828,455, supra; and U.S. Pat. No.5,978,085, supra.

In the case of other technologies that require multiple exposures tocreate a single FF that can produce an FPD value, we would practice thepresent invention by designating the multiple exposures as a singleexposure group and follow the method of this invention by using exposuregroups where exposures are called for in the two main embodiments ortheir extensions.

Heretofore we have specified this invention with the wafer notch anglesbeing specifically 180° and 270°. In practice, any two wafer notchangles differing by +90° or −90° could be used.

FIG. 24 is a block diagram illustrating a technique for processing thefinal output. As illustrated in FIG. 24, a resist coated wafer is loadedonto a scanner. In the example illustrated in FIG. 24 a scannerdiagnoses itself for defects in dynamic scan field curvature. Thedynamic scan field curvature information can then be used to correct thescanner, for example the scanner dynamic scan field curvature can beadjusted in response to the information. A reticle with focusingfiducials is also loaded onto the scanner. The scanner is thenprogrammed to expose the focusing fiducials onto the wafer in accordancewith a predetermined recipe from the method of this embodiment. Afterthe wafer has the desired pattern exposed on it, the exposed wafer issent through a photoresist track and developed. The developed wafer withthe pattern of focusing fiducials is then loaded onto the scanner. Thescanner is programmed to compute dynamic scan field curvature from thefocusing fiducial data measured using the scanner (Scanner A in FIG. 24)and provided dynamic lens field curvature values. The scanner thenoutputs the ZS and θ values.

FIG. 25 is a block diagram illustrating another technique for processingthe final output. In a manner similar to that described in FIG. 24, aresist coated wafer and a reticle with focusing fiducials are loadedonto a scanner. The focusing fiducials are then exposed onto the waferin accordance with a predetermined recipe from the method of thisembodiment. The exposed wafer is sent through a photoresist track anddeveloped. In this technique, the developed wafer with the pattern offocusing fiducials is then loaded onto a metrology tool, such as anoverlay reader. The metrology tool measures the developed fiducials andoutputs metrology data that is fed into a processor or computer thatconverts the raw metrology data into focusing fiducial values. Another(or possibly the same) computer processes the focusing fiducial data andprovided lens dynamic field curvature data to compute dynamic scan fieldcurvature. This computer then outputs the ZS and θ values.

The present invention has been mainly described with respect to itsapplication on the projection imaging tools (scanners) commonly used insemiconductor manufacturing today. See, for example, “Micrascan™ IIIPerformance of a Third Generation, Catadioptric Step and ScanLithographic Tool”, D. Cote et al., SPIE, Vol. 3051, pp. 806-816, 1997;“ArF Step and Scan Exposure System for 0.15 Micron and 0.13 MicronTechnology Node”, J. Mulkens et al., SPIE Conference on OpticalMicrolithography XII, pp. 506-521, March 1999; and “0.7 NA DUV Step andScan System for 150 nm Imaging with Improved Overlay”, J. V. Schoot,SPIE, Vol. 3679, pp. 448-463, 1999. The methods of the present inventioncan be applied to other scanning projection tools, such as 2-dimensionalscanners. See, for example, “Large Area Fine Line Patterning by ScanningProjection Lithography”, H. Muller et al., MCM 1994 Proceedings, pp.100-104, 1994; and “Large-Area, High-Throughput, High-ResolutionProjection Imaging System”, K. Jain, U.S. Pat. No. 5,285,236 issued Feb.8, 1994. Other scanning projection tools to which the invention can beapplied include office copy machines. See, for example, “ProjectionOptical System for Use in Precise Copy”, T. Sato et al., U.S. Pat. No.4,861,148 issued Aug. 29, 1989. The invention also can be applied tonext generation lithography (ngl) systems such as XUV, SCALPEL, EUV(Extreme Ultra Violet), IPL (Ion Projection Lithography), EPL (electronprojection lithography), and X-ray. See, for example, “Development ofXUV Projection lithography at 60-80 nm”, B. Newnam et al., SPIE, Vol.1671, pp. 419-436, 1992, (XUV); “Reduction Imaging at 14 nm UsingMultilayer-Coated Optics: Printing of Features Smaller than 0.1 Micron”,J. Bjorkholm et al, Journal Vacuum Science and Technology, B. 8(6), pp.1509-1513, November/December 1990)(EUV); “Mix-and-Match: A NecessaryChoice”, R. DeJule, Semiconductor International, pp. 66-76, February2000; and “Soft X-Ray Projection Lithography”, N. Ceglio et al., J. Vac.Sci. Technol., B 8(6), pp. 1325-1328. The present method can also beused with immersion lithography where the optical medium above the waferhas a refractive index significantly different from air (water forexample).

The present invention has been mainly described with respect to therecording medium being positive photoresist. The present invention couldequally well have used negative photoresist providing we makeappropriate adjustment to the box-in-box structures on the reticle. Ingeneral, the recording medium is whatever is typically used on thelithographic projection tool we are measuring. Thus, on an EPL tool, anelectron beam photoresist such as PMMA could be utilized as therecording medium. Thus, the recording media can be positive or negativephoto resist material, electronic CCD or diode array liquid crystal orother optically sensitive material.

So far, we have described the substrates on which the recording media isplaced as wafers. This will be the case in semiconductor manufacture.The exact form of the substrate will be dictated by the projectionlithography tool and its use in a specific manufacturing environment.Thus, in a flat panel manufacturing facility, the substrate on which therecording material would be placed would be a glass plate or panel. Amask making tool would utilize a reticle as a substrate. Circuit boardsor multi-chip module carriers are other possible substrates.

The techniques described can be used where the reticle, or mask, is achrome patterned glass reticle containing arrays of alignment marks. Inaddition the reticle can be a SCALPEL or EUV reticle containing arraysof alignment marks or a reflective mask.

The focusing fiducial can take many forms. For example, the focusingfiducials can be electronic test patterns, box-in-box, frame-in-frame,or segment-in-segment patterns. The focusing fiducials can also besegmented bar-in-bar patterns, Schnitzl patterns, FOCAL patterns, PSFMpatterns, or TIS alignment marks.

While the present invention has been described in conjunction withspecific preferred embodiments, it is evident that many alternatives,modifications and variations will be apparent to those skilled in theart in light of the foregoing description. It is therefore contemplatedthat the appended claims will embrace any such alternatives,modifications and variations as falling within the true scope and spiritof the present invention.

1. A method of determining dynamic scan field curvature associated witha photolithographic scanner having a projection lens, the methodcomprising: exposing an array of focusing fiducials in a reticle of thescanner onto a substrate coated with a suitable recording media;rotating and realigning the substrate; exposing a second array offocusing fiducials through the reticle, offset from the first exposedarray of focusing fiducials by a predetermined position to produce aprinted array of offset focusing fiducials; and calculating dynamic scanfield curvature in accordance with measurements of the focusingfiducials and a dynamic lens field curvature map for thephotolithographic scanner.
 2. A method as defined in claim 1, whereinthe array of focusing fiducials is a 2mx+1 by 2my+1 array.
 3. A methodas defined in claim 1, wherein the substrate is rotated 90 degrees.
 4. Amethod as defined in claim 1, wherein the offset between the first andsecond exposures is by an amount such that the substrate flatness overthe shifted distance does not vary beyond a desired amount.
 5. A methodas defined in claim 1, wherein the substrate is a semiconductor wafer.6. A method as defined in claim 1, wherein the substrate is a flat paneldisplay.
 7. A method as defined in claim 1, wherein the substrate is areticle.
 8. A method as defined in claim 1, wherein the substrate is anelectronic recording media.
 9. A method of determining dynamic scanfield curvature associated with a photolithographic scanner having aprojection lens and a scanner field that is longer in the scan directionas compared with the across-field direction, the method comprising:exposing an array of focusing fiducials in a reticle of the scanner ontoa substrate coated with a recording media; rotating the substrate andrealigning the substrate; exposing a second array of focusing fiducialsthrough the reticle to produce a printed array of focusing fiducials;shifting the substrate in a desired-direction by a desired amount;exposing a third array of focusing fiducials through the reticle toproduce a three-level printed array of focusing fiducials; andcalculating dynamic scan field curvature in accordance with measurementsof the focusing fiducials and a dynamic lens field curvature map for thephotolithographic scanner.
 10. A method as defined in claim 9, whereinthe array of focusing fiducials is a 2 mx+1 by 2my+1 array.
 11. A methodas defined in claim 9, wherein the substrate is rotated 90 degrees. 12.A method as defined in claim 9, wherein shifting the substrate is in anx-direction.
 13. A method as defined in claim 9, wherein the substrateis shifted a distance equal to an integral multiple of a spacing pitchof the focusing fiducials.
 14. A method as defined in claim 9, whereinthe shifted substrate is offset by a desired amount.
 15. A method asdefined in claim 14, wherein the offset is such that the substrateflatness over the shifted distance does not vary beyond a desiredamount.
 16. A method as defined in claim 9, wherein the substrate is asemiconductor wafer.
 17. A method as defined in claim 9, wherein thesubstrate is a flat panel display.
 18. A method as defined in claim 9,wherein the substrate is a reticle.
 19. A method as defined in claim 9,wherein the substrate is an electronic recording media.
 20. An apparatusfor determining dynamic scan field curvature of a photolithographicscanner, the apparatus comprising: a data interface that receives datataken from a developed substrate; and a processor configured to acceptmetrology data from the data interface wherein the data is obtained frommeasuring a substrate with exposed focusing fiducials and dynamic lensfield curvature data and to output dynamic scan field curvature inaccordance with focal plane deviation values based on measurements ofthe focusing fiducials on the substrate.
 21. A method as defined inclaim 20, wherein the substrate is a semiconductor wafer.
 22. A methodas defined in claim 20, wherein the substrate is a flat panel display.23. A method as defined in claim 20, wherein the substrate is a reticle.24. A method as defined in claim 20, wherein the substrate is anelectronic recording media.
 25. A photolithographic projection scannercomprising: a projection lens; a reticle stage and a substrate carrierthat can be positioned relative to each other; and a processor that cancontrol the projection scanner to position the reticle stage andsubstrate carrier in accordance with an exposure sequence, and adjustthe scanner in accordance with measurements of focusing fiducialsexposed on the substrate and a dynamic lens field curvature map so as tominimize the dynamic lens field curvature of the scanner.
 26. A scanneras defined in claim 25, whereby the measurements of the focusingfiducials are made on a measurement subsystem of the scanner.
 27. Ascanner as defined in claim 25, whereby the substrate carrier is asemiconductor wafer carrier.
 28. A method of controlling aphotolithographic projection scanner comprising: exposing an array offocusing fiducials in a reticle of the scanner onto a substrate coatedwith a suitable recording media; rotating and realigning the substrate;exposing a second array of focusing fiducials through the reticle,offset from the first exposed array of focusing fiducials by apredetermined position to produce a printed array of offset focusingfiducials; and determining dynamic scan field curvature in accordancewith measurements of the focusing fiducials and a dynamic lens fieldcurvature map for the photolithographic scanner; and adjusting thescanner in accordance with the determined dynamic scan field curvatureof the projection lens so as to minimize the effects of the dynamic scanfield curvature of the scanner.
 29. A method as defined in claim 28,whereby the substrate comprises a semiconductor wafer.
 30. A method ofmanufacturing a semiconductor chip, the method comprising: receivingdynamic scan field curvature of a projection lens used in a scanner; andadjusting the scanner in accordance with the received dynamic scan fieldcurvature of the projection lens so as to minimize the effects ofdynamic scan field curvature of the scanner while exposing asemiconductor substrate.
 31. A method as defined in claim 30, wherebythe received dynamic scan field curvature is determined in accordancewith measurement of focusing fiducials on a developed substrate and adynamic lens field curvature map.
 32. A method as defined in claim 31,whereby determining the dynamic scan field curvature further comprises:exposing an array of focusing fiducials in a reticle of the scanner ontoa substrate coated with a suitable recording media; rotating andrealigning the substrate; exposing a second array of focusing fiducialsthrough the reticle, offset from the first exposed array of focusingfiducials by a predetermined position to produce a printed array ofoffset focusing fiducials; and calculating dynamic scan field curvaturein accordance with measurements of the focusing fiducials and a dynamiclens field curvature map for the photolithographic scanner.